Question

Find a.b. IaI =3, IbI = 5 the angle between a and b is 2π/3

Answer 1

Answer: $a\cdot b= -7.5$

Step-by-step explanation:

Formula : If a and b be any two vector , then the dot product of and b is given by $a\cdot b= |a||b|\cos {\theta}$ , where $\theta$ is the angle between them.

As per given , we have

IaI =3, IbI = 5 $\theta =\dfrac{2\pi}{3}$

Then, $a\cdot b= (3)(5)\cos \dfrac{2\pi}{3}$

$a\cdot b= (15)\cos ( \pi-\dfrac{\pi}{3})$

$a\cdot b= (15)(-\cos \dfrac{\pi}{3})$ (∵ cos (π-x)=-cos x)

$a\cdot b= (15)(-\dfrac{1}{2})$  [∵$\cos \dfrac{\pi}{3}=\dfrac{1}{2}$ ]

$a\cdot b= -7.5$

Therefore , $a\cdot b= -7.5$